Question

Using the image method

An ideal electric dipole, of dipole moment p, is normally oriented to an infinite conductor plane, at a distance d from it. If the plane is "grounded", calculate:

1) The electrostatic potential at all points.

2) The load density induced in the plane.

Answer 1

The image of an electric dipole moment p at above an infinite grounded conducting plane in the xy-plane is a dipole moment at with equal magnitude and direction rotated azimuthally by π. That is, a dipole moment with Cartesian components will have in image dipole moment . The dipole experiences a force in the z direction, given by

and a torque in the plane perpendicular to the dipole and the conducting plane,

If the dipole is pictured as two large charges separated by a small distance, then the image of the dipole will not only have the charges modified by the above procedure, but the distance between them will be modified as well.